Triad of Equivalence Theorems for the Radiant Intensity of Partially Coherent Beams on Scattering

TL;DR

This paper introduces a novel triad of equivalence theorems for the radiant intensity of partially coherent beams on scattering, expanding the understanding beyond existing plane wave theories and aiding inverse scattering applications.

Contribution

It presents the first equivalence theory for partially coherent beams on scattering, revealing a triad of theorems that generalize and extend previous plane wave results.

Findings

Established necessary and sufficient conditions for equivalent scattered fields.

Identified a triad of equivalence theorems for partially coherent beams.

Showed existing plane wave theory as a special case of the triad.

Abstract

By using Laplace's method for double integrals and the so-called beam condition obeyed by a partially coherent beamlike light field, we report the equivalence theory (ET) of partially coherent beams on scattering for the first time. We present the necessary and sufficient condition for the two scattered fields that have the same normalized radiant intensity distribution when Gaussian Schell-model beams whose effective beam widths are much greater than the effective transverse spectral coherence lengths are scattered by Gaussian Schell-model media. We find that the condition contain three implications, and each of them corresponds to a statement of an ET of radiant intensity in a scattering scenario, which exposes the concept of a previously unreported triad of ETs for the radiant intensity of partially coherent beams on scattering. We further find that the existing ET of plane waves on scattering, which only asserts that two scatterers with scattering potentials' correlations whose low-frequency antidiagonal spatial Fourier components are identical, essentially is merely the first member of our triad of ETs, while the other two hidden important members are completely ignored. Our findings are crucial for the inverse scattering problem since they contribute to avoid possible reconstruction errors in realistic situations, where the light field used to illuminate an unknown object is a partially coherent beam rather than an idealized plane wave.